Abstract
We present an introduction to some concepts of Bayesian data analysis in the context of atomic physics. Starting from basic rules of probability, we present the Bayes’ theorem and its applications. In particular we discuss about the limits of classic statistics methods and in which cases a Bayesian analysis is mandatory. Moreover, we show how probability values can be assigned to different possible models (different numbers of peaks, type peak profile, etc.) from the analysis of experimental data.
Highlights
The standard analysis of atomic spectra consist on comparing n pairs {xi, yi} of measured values to the values of a function F (xi, a) used to model the data, where a are the function parameters
The common practice to determine the set of parameters abest that describes at best the data is to find the maximum of the likelihood function n
For a better insight in the implication of this theorem, we consider the particular case where X represent the hypothesis that the parameter values set a truly describes the data (via the function F (x, a)) and where Y correspond to the recorded data {xi, yi}
Summary
The standard analysis of atomic spectra consist on comparing n pairs {xi, yi} of measured values (or {xi, yi, σi} triplets if error bars are available) to the values of a function F (xi, a) used to model the data, where a are the function parameters. They have some limitations that one should be aware: i) Cause-effect inversion: The maximum likelihood method is based on the probability L(a) = P ({xi, yi, σi}|a) to obtain certain data values for a given set of parameters a. For a better insight in the implication of this theorem, we consider the particular case where X represent the hypothesis that the parameter values set a truly describes the data (via the function F (x, a)) and where Y correspond to the recorded data {xi, yi}.
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